The monomorphism problem in free groups - Mathematics > Group Theory

Abstract: Let $F$ be a free group of finite rank. We say that the monomorphism problemin $F$ is decidable if for any two elements $u$ and $v$ in $F$, there is analgorithm that determines whether there exists a monomorphism of $F$ that sends$u$ to $v$. In this paper we show that the monomorphism problem is decidableand we provide an effective algorithm that solves the problem.